The primary difference between symmetric and asymmetric Encryption (& decryption) is the number of keys used in the process. While Symmetric encryption uses only a single key to perform both the tasks (i.e. encrypt & decrypt data) it works more like a lock & key situation where anyone who has the key can choose to encrypt or decrypt data as & when they want. The system is only as secure as your key and there is very little control over the process.

Whereas, in asymmetric encryption, a pair of (mathematically related) keys is used for either function. The system only knows it has to react to a mathematics function with a key. Depending upon the situation, the keys can be used in either direction. e.g. if a public key is used to encrypt data, only a private key can decrypt it. the same can be implemented in reverse i.e. a private key used to encrypt data and public key is used to decrypt it. both have their own use cases but in a nutshell, the same key can not be used for both purposes. One key will encrypt and the other will decrypt.